A method and a system for facilitating garbage collection (GC) operations in a memory-management system that supports both mark-sweep (MS) objects and reference-counted (RC) objects, wherein objects which are frequently modified are classified as MS objects, and objects which are infrequently modified are classified as RC objects. During a marking phase of a GC operation, the system identifies a set of root objects and then marks referents of the root objects. The system then recursively traverses referents of the root objects which are MS objects and while doing so, marks referents of the traversed MS objects. However, if an RC object is encountered during the traversal of an MS object, the system marks the RC object but does not recursively traverse the RC object. In doing so, the system avoids traversing a large number of RC objects which are infrequently modified.